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Embedding of a Banach algebra $A$ into $L(A')$


Author: Etienne Desquith
Journal: Proc. Amer. Math. Soc. 124 (1996), 2773-2778
MSC (1991): Primary 46H15
DOI: https://doi.org/10.1090/S0002-9939-96-03335-7
MathSciNet review: 1327005
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Abstract: Given a Banach space $X$, we have shown in 1994 that a product can be defined on it in such a way that the resulting Banach algebra is isomorphic to a compact subalgebra of the algebra $L(X')$ of all bounded linear operators on the topological dual $X'$ of $X$. Our purpose here is to prove that, more generally, any Banach algebra $A$ admitting a left approximate identity, is isomorphic to a subalgebra of $L(A')$, the isomorphism being isometric, provided the approximate identity is bounded by 1. As a consequence, we get a factorization through $L(A')$, of the elements in $A'$.


References [Enhancements On Off] (What's this?)

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Additional Information

Etienne Desquith
Affiliation: Institut de Recherches Mathématiques (IRMA), 08 BP 2030 Abidjan 08, Cote D’Ivoire

DOI: https://doi.org/10.1090/S0002-9939-96-03335-7
Received by editor(s): September 29, 1994
Received by editor(s) in revised form: March 13, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society

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